This paper presents a novel guidance and control strategy for the efficient capture and stabilization of fast-spinning target satellites, such as spin-stabilized models, utilizing a spinning-base servicing satellite equipped with a robotic manipulator, joint locks, and reaction wheels (RWs). The proposed method leverages the RWs of the servicing satellite to replicate the target satellite's spin dynamics, while locking the manipulator joints to achieve precise spin-matching. This technique effectively neutralizes the target's relative motion, simplifying the capture trajectory planning and eliminating the need for post-capture adjustments. Following spin-matching, the manipulator's joints are unlocked, enabling a coordinated control system to execute the capture maneuver while maintaining zero relative rotation between the servicing and target satellites. Upon successful capture, the system transitions into the spin stabilization phase. Here, the joints are re-engaged to create a unified tumbling rigid body composed of the interconnected satellites. An optimized control system then applies negative torques through the RWs to rapidly dampen the tumbling motion, constrained by the actuation limits of the RWs and the manipulator's end-effector torque capabilities.